Dianzi Liu V assili V Toropov Osvaldo M Querin University of Leeds Content Introduction Topology Optimisation Parametric Optimisation ID: 292098
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Slide1
Topology and Parametric Optimisation of a Lattice Composite Fuselage Structure
Dianzi
Liu,
V
assili
V.
Toropov
,
Osvaldo M.
Querin
University
of Leeds
Slide2
Content
IntroductionTopology Optimisation
Parametric Optimisation
ConclusionSlide3
Topology Optimisation
MethodTopology Optimisation is a computational means of determining the physical domain for a structure subject to applied loads and constraints.The method used in this research is the Solid Isotropic Material with Penalization (SIMP).
It works by minimising the compliance (maximising global stiffness) of the structure by solving the following optimization problem:
for a single load case,
or by minimising the weighted compliance for multiple (
N
) load cases:Slide4
Topology Optimisation: minimizing the compliance of the structure for 3 load cases
Load cases consist of distributed loads over the length and loads at the barrel end(shear forces, bending moments and torque)
Question: what are the appropriate weight coefficient values?
Topology Optimisation
Load
C
asesSlide5
Topology Optimisation
Method for weight allocationThe following strategy was used:Do topology optimization separately
for each
load case, obtain
the corresponding
compliance values
Allocate the weights to the individual compliance components (that correspond to the individual load cases) in the same proportionThe logic behind this is as follows: if for a particular load case topology optimization produced a relatively high compliance value, then this load case is a critical one and hence it should be taken with a higher weight in the total weighted
compliance optimization problemSlide6
Topology Optimisation Results for 3 load cases
Topology OptimisationModel and Results
Bending
Torsion
Transverse bendingSlide7
Topology Optimisation
Results
Iso
view
:
optimization
of the barrel for weighted complianceSlide8
Optimization
of the barrel without windows (Top) and with windows (Bottom)Two backbones on top and bottom of the barrelNearly +-45° stiffening on the side panelResult: beam structure for the barrel
Note: SIMP approach does not consider buckling
Topology Optimisation
Presence of window openingsSlide9
Development of the Design Concept by DLR
Reflection on the layout of the “ideal” structure from the topology optimization it in the aircraft design contextConsideration of airworthiness and manufacturing requirements
Fuselage design concept developed by DLR
High potential for weight savings achievable due to new material for stiffeners and non-rectangular skin bays
Due to large number of parameters in the obtained concept a multi-variable optimisation should be performedSlide10
Multi-parametric Optimisation
Method: the multi-parameter global approximation-based approach used to solve the optimization problem
P
roblem
: optimize an
anisogrid composite fuselage
barrel with respect to weight and stability, strength, and stiffness using 7 geometric design variables, one of which is an integer variable.Procedure: develop a set of numerical experiments (FEA runs) where each corresponds to a different combinations of the design variables. The concept of a uniform Latin hypercube Design of Experiments (DOE) with 101 experiments (points in the variable space) was used. FE analysis of these 101 fuselage geometries was performed global
approximations built as explicit expressions of the design variables using Genetic Programming (GP) parametric optimisation
of the fuselage barrel by a Genetic Algorithm (GA) verification of the optimal solution by FE simulation 10Slide11
Design of Experiments
In order to generate the sampling points for approximation building, a uniform DOE (optimal Latin hypercube design
) is proposed.
The main principles in this approach are as follows:
The number of levels of factors (same for each factor) is equal to the number of experiments and for each level there is only one experiment
;
The points of experiments are distributed as uniformly as possible in the domain of factors, which are achieved by minimizing the equation: where Lpq is the distance between the points p
and q (p≠q) in the system.
11
Example: A 100-point DOE generated
by an optimal
Latin hypercube techniqueSlide12
Genetic Programming
Genetic
Programming (GP) is a symbolic regression technique, it produces an
analytical expression
that provides the best fit of the
approximation
into the data from the FE runs. Example: a approximation for the shear strain obtained from the 101 FE responses:
12where Z1, Z2, …, Z7 are the design
variables.
Indications of the quality of fit of the obtained expression into the data:Slide13
FEM Modeling and Simulation
13
Automated Multiparametric Global Barrel FEA Tool:
Modeling, Analysis, and Result Summary
Displacement
Skin Strains
Beam Strains
Buckling
Results:
Results of all analyzed models are summarized in a separate file
Session file:
List of Models to be Analyzed
Modeling and Analysis
PCL Function
Post-processing
PCL Function
User Defined Parameters:
-Geometry
-Loads
-Materials
-Mesh seed
MSC Patran
MSC Nastran
PCLSlide14
x
y
z
Q
z
Optimisation
of the Fuselage Barrel
Composite skin and stiffeners
14
An upward gust load case at low altitude
and cruise speed
Undisturbed anisogrid fuselage barrel
Early design
stageSlide15
Variables and Constraints
Design variables
Lower bound
Upper bound
Skin thickness (h)
0.6 (mm)
4.0 (mm)
Number of helix rib pairs around the circumference, (n)
50
150
Helix rib thickness, (t
h
)
0.6 (mm)
3.0 (mm)
Helix rib height, (
H
h
)
15.0
(mm)
30.0
(mm)
Frame pitch, (d)
500.0
(mm)
650.0
(mm)
Frame thickness, (
t
f
)
1.0 (mm)
4.0 (mm)
Frame height, (
H
f
)
50.0
(mm)
150.0
(mm)
15
H
f
t
f
W
f
=20mm
W
f
=20mm
H
h
W
h
=20mm
d
h
=8mm
d
h
=8mm
t
h
Circumferential
Frames
Helix Ribs
Frame Pitch, d
Circumf
.
Helix Rib
Pitch, dep. on n
2φ
Fuselage
Geometry
Radius
2m
h
Barrel Cross Section
Constraints:
Strength: strains in the skin and in the stiffeners
Stiffness: bending and torsional stiffness
Stability: buckling
Normalization
Normalized mass against largest mass
Margin of safety ≥0
Strain
Stiffness
Buckling
Variables:Slide16
Results: Summary of parametric optimisation
16
Model
Tensile Strain (MS)
Compressive Strain (MS)
Shear Strain (MS)
Buckling (MS)
Torsional
Stiffness (MS)
Bending Stiffness (MS)
Normalized mass
Prediction I
0.02
0.00
1.42
---
---
---
0.10
Optimum
I
0.36
-0.09
1.21
---
---
---
0.11
Prediction II
0.03
0.01
1.64
---
---
---
0.11
Optimum
II
0.54
0.04
1.54
---
---
---
0.12
Prediction III
0.20
0.23
1.27
0.00
1.21
0.89
0.29
Optimum
III
0.62
0.08
1.09
-0.07
1.21
0.89
0.29
Comp. Des.
1.15
0.19
1.31
-0.04
1.25
0.81
0.29
Design
Skin thickness (h)
, mm
Nr. of helix rib pairs, (n)
Helix rib thickness, (t
h
)
, mm
Helix rib height, (
H
h
)
, mm
Frame pitch, (d)
, mm
Frame thickness, (
t
f
)
, mm
Frame height, (
H
f
)
, mm
Optimum I
2.0860.000.60
27.90627.701.0050.00Optimum II2.2860.00
0.6627.90627.701.0050.00Optimum III1.71
150.000.6127.80501.701.0050.00Strength Contraint
Stability, Strength, and Stiffness Contraints
Optimum III geometry with realistic ply layup:
Helical ribs
: tall and slender Frames: thin and small 209 mm628 mm18.94 °Optimum II84 mm502 mm9.55 °Optimum III and Comp. Design(±45,0,45,0,-45,90)s, 14 plies, total thickness = 1.75 mmSlide17
Results: Interpretation of the skin as a laminate, 14 plies
17
Stacking sequence
Buckling (MS)
Torsional Stiffness
Bending Stiffness
Normalized mass
(±45,0,45,0,-45,90)
s
-0.04
1.25
0.81
0.29
(±45,0,45,90,-45,0)
s
0.04
1.25
0.81
0.29
(±45,90,45,0,-45,0)
s
0.13
1.25
0.81
0.29
% of 0° plies
% of +/-45° plies
% of 90° plies
28.6%
57.1%
14.3%Slide18
Results: Interpretation of the skin as a laminate, 15 plies
18
Stacking sequence
Buckling (MS)
Torsional Stiffness
Bending Stiffness
Normalized mass
(±45,0,45,0,-45,90)
s
,0
0.12
1.26
0.92
0.30
(±45,0,45,90,-45,0)
s
,0
0.20
1.26
0.92
0.30
(±45,90,45,0,-45,0)
s
,0
0.28
1.26
0.92
0.30
% of 0° plies
% of +/-45° plies
% of 90° plies
33.3%
53.3%
13.3%Slide19
Conclusion
Multi-parameter global metamodel-based optimization was used for:Optimization of a composite anisogrid fuselage barrel with respect to weight, stability, strength, stiffness using 7 design variables, 1 being an integer
101-point uniform design of numerical experiments, i.e. 101 designs
analysed
Automated Multiparametric Global Barrel FEA Tool generates responses
global approximations built using Genetic Programming (GP)
parametric optimization on global approximationsoptimal solution verified via FE Overall, the use of the global metamodel
-based approach has allowed to solve this optimization problem with reasonable accuracy as well as provided information on the structural behavior
of the anisogrid design of a composite fuselage.There is a good correspondence of the obtained results with the analytical estimates of DLR, e.g. the angle of the optimised triangular grid cell is 9.55° whereas the DLR value is 12°
19Slide20
20
Thank You
for your Attention